1. Field of the Invention
The present invention concerns a method for determination of coefficients of a diffusion tensor by means of magnetic resonance for description of a diffusion process within a subject, in which spatially-resolved, variously diffusion-coded diffusion data are generated from volume elements of the subject dependent on control data for various diffusion codings in chronological order.
The invention likewise concerns a device for implementation of the method.
2. Description of the Prior Art
A method and a device of the aforementioned type are known from U.S. Pat. No. 5,539,310. The method specified therein is based on a magnetic resonance measurement sequence proposed by Stejskal and Tanner in 1965. The method described in U.S. Pat. No. 5,539,310 expands the measurement sequence proposed by Stejskal and Tanner such that coefficients or elements of a diffusion tensor are determined and graphically represented for each voxel in an examination region. A clear representation with a diffusion ellipsoid, the main axis of which represents the direction of the strongest diffusion process, ensues. The expansion in the individual directions stands for a numerical value of the diffusion process in the corresponding directions. In medical applications, the relative mobility of water molecules in endogenic tissue can thus be measured with magnetic resonance diffusion imaging. Since the diffusion in the tissue can depend on its structure (such as, for example, the fiber direction), medically-relevant conclusions can be derived from the diffusion tensor.
The diffusion data are determined in the magnetic resonance measurement from the size and direction of the diffusion gradient fields used for diffusion coding. Strong gradient pulses are thereby used that are oriented symmetrically to a radio-frequency, 180° refocusing pulse. The first gradient pulse before the 180° refocusing pulse generates a phase shift for all spins; the second gradient pulse inverts this phase shift. Given stationary molecules (protons in medical imaging), the phase shift therewith cancels again. However, for molecules that, due to Brownian motion, are located at a different location during the effect of the second gradient pulse than during the effect of the first gradient pulse, the phase shift is not completely compensated. A rest phase displacement remains that leads to a signal attenuation. The diffusion coding can be controlled by the size and direction of such gradient pulses.
In medical diffusion tensor measurement by means of magnetic resonance techniques and the subsequent graphical representation (DTI=Diffusion Tensor Imaging), large quantities of measurement data accumulate, from which the sought six tensor parameters or tensor coefficients (thus the independent elements or components of a symmetrical 3×3 tensor matrix) are calculated per voxel. The tensor parameters are subsequently used to calculate relevant parameter cards for the diagnostics. For example, the isotropic portion of the diffusion tensor or the anisotropic portion of the diffusion tensor is displayed in corresponding parameter cards (Average Apparent Diffusion Coefficient Map or ADCav Map, or Fractional Anisotropy Map or FA Map). Due to the large amount of measurement data, the calculation of the diffusion tensor per voxel requires the determination of the unknown parameters by means of a compensation. Methods known from multi-variant linear regression are used, for example methods that form a pseudo-inverse or implement a singular value decomposition. These methods are, however, very storage-space intensive and computationally complex because all data for the evaluation are retained in the known methods and the sought parameters are only determined by means of compensation methods after conclusion of the measurement. Rules for accounting for the intensity values are also applied as alternatives for specific, rigid sets of diffusion codings. However, such methods are very inflexible.